Consider the following portfolio choice problem. The investor has initial wealth w andutility u(x) = -e-ª. There is a safe asset (such as a US government bond) that has netreal return of zero. There is also a risky asset with a random net return that has onlytwo possible returns, R1 with probability 1 - q and Ro with probability q. We assumeR1 < 0, Ro > 0. Let a be the share of wealth w invested in the risky asset, so that 1 – ashare of wealth is invested in the safe asset.(a) Find a as a function of w. How does a change with wealth? Explain the intuition.(b) Another investor has the utility function u(x) =wealth? Explain the intuition.In(x). How does a change with(c) Calculate relative risk aversion for two investors using the utility functions in (a)and (b). How do they depend on wealth? How does this account for the qualitativedifference in the answers youu obtain in parts (a) and (b)!

Answered: Image /qna-images/answer/5b3f55e9-abaf-4304-b3e3-984ec85de6e4.jpg

Answered: Consider the following portfolio choice…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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An investor has decided to commit no more than $80,000 to the purchase of the common stocks of two companies, Company A and Company B. He has also estimated that there is a chance of at most a 1% capital loss on his investment in Company A and a chance of at most a 4% loss on his investment in Company B, and he has decided that these losses should not exceed $2000. On the other hand, he expects to make a(n) 15% profit from his investment in Company A and a(n) 18% profit from his investment in Company B. Determine how much he should invest in the stock of each company (x dollars in Company A and y dollars in Company B) in order to maximize his investment returns. What are the (x,y) values? What is the optimal profit?
An investor has decided to commit no more than $80,000 to the purchase of the common stocks of two companies, Company A and Company B. He has also estimated that there is a chance of at most a 1% capital loss on his investment in Company A and a chance of at most a 4% loss on his investment in Company B, and he has decided that these losses should not exceed $2000. On the other hand, he expects to make a(n) 15% profit from his investment in Company A and a(n) 18% profit from his investment in Company B. Determine how much he should invest in the stock of each company (x dollars in Company A and y dollars in Company B) in order to maximize his investment returns.(x, y)= What is the optimal profit?$
Mike, a lumber wholesaler, is considering the purchase of a (railroad) car- load of varied dimensional lumber. He calculates that the probabilities of reselling the load for $10,000, $9000, and for $8000 are 0.22, 0.33, and 0.45 respectively. In order to ensure an expected profit of $3000, how much can Mike pay for the load
52. Consider two securities, the first having μ1 = 1 and σ1 = 0.1, and the secondhaving μ2 = 0.8 and σ2 = 0.12. Suppose that they are negatively correlated,with ρ = −0.8.a. If you could only invest in one security, which one would you choose, andwhy?b. Suppose you invest 50% of your money in each of the two. What is yourexpected return and what is your risk?c. If you invest 80% of your money in security 1 and 20% in security 2, whatis your expected return and your risk?d. Denote the expected return and its standard deviation as functions of π byμ(π ) and σ (π ). The pair (μ(π ), σ (π )) trace out a curve in the plane as πvaries from 0 to 1. Plot this curve.e. Repeat b–d if the correlation is ρ = 0.1
Calculate the conditional expectation of Y when X = 2. E(YX2)
The table here shows the no-arbitrage prices of securities A and B that we calculated.Cash Flow in One YearSecurity Market Price Today Weak Economy Strong EconomySecurity A 231 0 600Security B 346 600 0a. What are the payoffs of a portfolio of one share of security A and one share of security B?b. What is the market price of this portfolio? What expected return will you earn from holdingthis portfolio?
Suppose that spot and futures prices of the underlying asset when hedge is initiated are $3.10 and $2.50 respectively, and when hedge is closed out are $2.90 and $2.80 respectively. 1. What is the meaning of above numbers? 2. What is the basis risk when hedge is initiated? 3. What is the basis risk when hedge is closed out? 4. Is it a perfect hedge? 5. What will be the effective price received (paid) for the hedging asset? (S₂ + F₁-F₂
Use the following two tables to answer questions a. - e. a. Which of the above securities cannot lie on the efficient frontier? b. Why might you nonetheless include it in your portfolio? c. What is the expected return for a portfolio comprised of 40% security B and 60% security C? d. What is the standard deviation for a portfolio comprised of 40% security B and 60% security C? e. Suppose a risk-free asset with a yield of 3% exists, but only for lending. Would the highly risk-averse investor's optimal portfolio be likely to contain asset C? Why or why not?
Given the following payoff table with the profits ($m), a firm might expect alternative investments (A, B, C) under different levels of interest rate (attached) (a) Which alternative should the firm choose under the maximax criterion? (b) Which option should the firm choose under the maximin criterion? (c) Which option should the firm choose under the LaPlace criterion? (d) Which option should the firm choose with the Hurwicz criterion with α = 0.2? (e) Using a minimax regret approach, what alternative should the firm choose? (f) Economists have assigned probabilities of 0.35, 0.3, and 0.35 to the possible interest levels 1, 2, and 3 respectively. Using expected monetary values, what option should be chosen and what is that optimal expected value? (g) What is the most that the firm should be willing to pay for additional information? Use Expected Regret (h) Use the alternative method to verify EVPI
Prove that a one-period binomial model is free of arbitrage if and only if d < r+1 < u u = S1(H)/S0 , d=S1(T)/S0
Consider the following payoff matrix.
A bank faces two types of borrowers, type A and B. Both want a $225 loan. Type A repays the loan 100% of the time and type B only repays with probability 0.66. The bank doesn't observe type, but believes fraction x is type A. What does x need to be so that the bank can afford a pooling interest rate of 25%? A) 0.51 B) 0.47 C) 0.41 D) 0.36

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